Copy the proof, mark the givens in the diagram and fill in the blanks to complete the proof
Answer:
Step-by-step explanation:
Draw UT Construction
UT = UT Reflexive Property
BT = EU Given
BU = ET Given
ΔUBT = ΔEUT SSS = SSS
<B = <E CPCTC
The bolded parts are the blanks you need to fill in.
Answer:
Draw UT construction
UT = UT reflexive property
BT = EU given
BU = ET given
ΔUBT = ΔEUT SSS = SSS
<B = <E CPCTC
hope this helps!
Point A and B are respectively 20m north and 48m east of point c.find the distance AB
Answer:
[tex]\boxed {AB = 52 m}[/tex]
Step-by-step explanation:
This forms a right triangle.
Therefore, by using the Pythagorean Theorem, we can find AB.
AB = √AC² + BC²
AB = √(20)² + (48)²AB = √400 + 2304AB = √2704AB = 52mI hope it helped you solve the problem.
Good luck on your studies!
Answer: Distance AB = 52 m
Step-by-step explanation:
Given information
Point A = 20 m north of point C
Point B = 48 m east of point C
Please refer to the attachment below for a graphical understanding
Concept
According to the graph drawn, Point A, Point B, and Point C form a right angle, and the distance between Point A and B would form a right triangle.
Therefore, we can use the Pythagorean theorem to find the distance between points A and B.
Given formula
a² + b² = c²
a = distance between point A and point Cb = distance between point B and point Cc = distance between point A and point BSubstitute values into the formula
a² + b² = c²
(20)² + (48)² = c²
Simplify exponents
400 + 2304 = c²
Simplify by addition
2704 = c²
c = √2704
c = 52 or c = -52 (reject, since no distance can be negative)
Therefore, the distance AB is [tex]\Large\boxed{52~m}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The coefficient of 8 • 2N is
Answer:
16
Step-by-step explanation:
when we multiply we have 16n so thats is d coefficient
1. Transform each blue piece so that the boat changes from blue to red. Try to use as few transformations as possible to complete the task! 2. TIP: Be sure to move the blue pieces so that the corresponding letters match at the same point. 3. Write down the specific stops you made to transform the shapes in your notebook.
a. What transformations would you use on the blue segments CD to get it to match with the red segments C2D2? Explain your movement using the coordinates of the vertices.
b. What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
c. Which line segments on the boat are parallel? Explain your answer.
d. Which line segments on the boat are perpendicular? Explain your answer.
e. Which line segments on the boat have a slope of 0? Explain your answer.
f. Which line segments on the boat have an undefined slope? Explain your answer.
7. What is the slope of ED? Explain your answer using the change in coordinates given that E is at (-11, 4) and D is at (-10, 5).
A) Rotate by 90° counterclockwise.
B) Reflection transformation about the line y = 5.
C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.
D) Perpendicular lines are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁
F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.
G) Slope of Line ED = 1
How to carry out Transformations?A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.
B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.
C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.
D) The line segments that are perpendicular are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.
F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.
G) Slope of ED = (5 - 4)/(-10 - (-11))
Slope of ED = 1/1
Slope = 1
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Suppose the probability that the instructor asks Sam, one of your classmates, is 0.05 and the probability that she/he asks John, another student in your class, is 0.07. What is the probability that the instructor asks one of these two students
The probability that the instructor asks one of Sam and John whose probabilities of being asked are as indicated in the task content is; 0.12.
What is the probability that the instructor asks one of these two students?It follows from the task content that the probability that Sam is being asked is; 0.05 while that for John being asked is; 0.07.
Consequently, we may conclude that the probability of either of the two classmates being asked the question in discuss is; the sum of the probabilities and hence, we have;
P(Sam or John) = 0.05 + 0.07
= 0.12.
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Please help me with this geometry question
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
HJ = 23.5 in[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = x, GH = y and GJ = z
x = y + 2z = x + y - 17x + y + z = 73put the value of x from equation 1 in equation 2
[tex]{ \qquad❖ \: \sf \:z = (y + 2) + y - 17} [/tex]
[tex]{ \qquad❖ \: \sf \:z = 2y - 15} [/tex]
now, put the value of x and z in equation 3
[tex]{ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73} [/tex]
[tex]{ \qquad❖ \: \sf \:4y - 13 = 73} [/tex]
[tex]{ \qquad❖ \: \sf \:4y = 86} [/tex]
[tex]{ \qquad❖ \: \sf \:y = 21.5 \: \: in} [/tex]
Now, we need to find HJ (x)
[tex]{ \qquad❖ \: \sf \:x = y + 2} [/tex]
[tex]{ \qquad❖ \: \sf \:x = 21.5 + 2} [/tex]
[tex]{ \qquad❖ \: \sf \:x = 23.5 \: \: in} [/tex]
[tex]{ \qquad \large \sf {Conclusion} :} [/tex]
HJ = 23.5 inIn a population where 81 % of voters prefer Candidate A,
an organization conducts a poll of 15 voters. Find the
probability that 11 of the 15 voters will prefer Candidate
The probability of 11 voters out of 15 voting candidate A is 0.9770
According to the statement
we have given that the percentage of voters is 81% and poll conducts are 15 and we have to find the probability that 11 of the 15 voters will prefer Candidate
So, For this purpose,
the question in based on binomial probability which means the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes p and q and p+q=1
let probability of choosing candidate A be p
and probability of choosing candidate B be q
In question p=0.81 and q=0.16
n be total number of voters=15
x be number of successes
then P(x=x)= [tex]\frac{n}{x} p^{x} q^{n-x}[/tex]
P(x=11)= [tex]\frac{11}{15} 0.81^{11} 0.16^{4}[/tex]
= 0.9770
So, the probability of 11 voters out of 15 voting candidate A is 0.9770
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HELP PLEASE will give brainliest
Answer:
This is an example of correlation because there is an obvious relationship between the two scenarios
Step-by-step explanation:
This is not cause-and-effect therefore cannot be causation or "cause"
(x^2-y^2)dx+2xydy=0
so this is a problem of a differential equation I've been trying so hard to match with the given answer but failed every time I tried. So, is there anyone who can really can help me out to catch the mistakes that I'm making?
* The last line of my workout is just a dump guess.
The pictures are my workouts also the answer to this question is attached. Please read my solutions by this order : pic-1, pic-3 & pic-2, if necessary.
[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]
Multiply both sides by [tex]\frac1{x^2}[/tex].
[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]
Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].
[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]
[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]
Separate the variables.
[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]
[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]
Integrate both sides
[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]
On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].
[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]
[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].
[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]
[tex]w = e^C e^{\ln|x^{-1}|}[/tex]
[tex]w = Cx^{-1}[/tex]
[tex]1 + v^2 = Cx^{-1}[/tex]
[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]
[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]
Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)
You incorrectly combine the fractions on the left side.
[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]
Mr. Black bought a television set for $450.00. He later sold the television set at a loss of 30%. (a) Calculate the amount of the loss.
The amount of the loss exists 1350.
What is the amount of loss?
Amount of Loss means an amount equivalent to the outstanding balance of the principal amount, less any amounts recognized by perfecting rights under a security agreement, together with such interest as the executive director shall permit, to a maximum of such interest as may be permitted by rule.
Given: Mr. Black purchased a television set for $450.00. He subsequently sold the television set at a defeat of 30%.
From the given information, we get
[tex]$4500\cdot \frac{30}{100}[/tex]
simplifying, we get
[tex]$4500\cdot \frac{30}{100}[/tex]
= 1350
Therefore, the amount of the loss exists 1350.
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A book sold 42,600 copies in its first month of release. Suppose this represents 9.2% of the number of copies sold to date. How many copies have been sold to date?
Answer:
We lend 100% - 9.2% and this will equal 90.8%, then we will make this percentage of 42,600 which will give us 38,680 and we will add the 42,600 and this will give us a total of 81,460 copies.
A survey was done with 205 women. Each women was asked how many children she had. The results showed that 28% of the women had 3 or more children. How many surveyed women had less than 3 children?
David signed up to provide snacks for his daughter and her school group's camping trip. He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days. He also wanted to buy some boxes of fruit snacks, which were $4 each. He just needed to decide how many to buy, and then figure the total cost.
Select the expression that will help him to determine the total cost.
The expression that will help him to determine the total cost is as follows:
y = 60 + 4x
How to construct an expression?He signed up to provide snacks for his daughter and her school group's camping trip.
He found a package of granola bars in bulk for $60 that he thought would be enough for everyone for a few days.
He also wanted to buy some boxes of fruit snacks, which were $4 each.
The number to buy and the total cost can be expressed as follows:
let
y = total cost
x = number of boxes of fruit juice.
Therefore, the expression that will help him to determine the total cost is as follows:
y = 60 + 4x
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use yours formula to find the missing number of faces edges 15 vertices 9
Using Euler's Formula, the number of faces is given by: 8.
What does Euler's Formula states?It states that the number of vertices, edges and faces is related by the following equation:
V - E + F = 2.
In this problem, the parameters are given as follows:
E = 15, V = 9.
Hence the number of faces is given by:
V - E + F = 2.
9 - 15 + F = 2
F - 6 = 2
F = 8.
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What is the area of the actual square window
shown in the scale drawing?
0.75 in.
Scale
1 in. = 2 m
Answer: 2.25 meters
Step-by-step explanation: 1 in = 2 meters. 0.75 is 75 percent of 1 so the length of the window is 75 percent of 2 which is 1.5. 1.5 squared is 2.25 so the length of the window is 2.25 meters
A Community theater sold 63 tickets to the afternon fora total of 444 birr, an adult ticket Cost 8 birr achild ticket cost 4 bir, and a senior ticket cost 6 birr. If twice as many tickets were sold to adults as to Children and seniors combined how many of each tick were sold ? ( Use Gaussian elimination method)
The number of tickets sold are:
30 children tickets were sold33 adult tickets were soldHow to determine the number of tickets sold to children and seniors?From the question, we have the following parameters:
Number of tickets = 63
Total amount = 444 Birr
Adult ticket = 8 Birr per adult
Children ticket = 6 Birr per adult
Represent the children tickets with x and adults ticket with y.
So, we have the following system of equations
x + y = 63
6x + 8y = 444
Express the equations as a matrix
x y
1 1 63
6 8 444
Apply the following transformation
R2 = R2 - 6R1
This gives
x y
1 1 63
0 2 66
Apply the following transformation
R2 = 1/2R2
x y
1 1 63
0 1 33
From the above matrix, we have the following system of equations
x + y = 63
y = 33
Substitute y = 33 in x + y = 63
x + 33 = 63
Subtract 33 from both sides of the above equation
x = 30
Hence, 30 children tickets were sold and 33 adult tickets were sold
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each of the two equal angles of an isosceles triangle is half the third angle find the angles of the triangle
Answer:
Two Equal Angles = 45°
Third Angle = 90°
Step-by-step explanation:
Given information
Two equal angles of an isosceles triangle are half the third angle
Set variables
Let x be the angle of the equal angles of the isosceles triangle
Let 2x be the angle of the third angle
Set equations
x + x + 2x = 180 (Triangle angle sum theorem)
Combine like terms
2x + 2x = 180
4x = 180
Divide 4 on both sides
4x / 4 = 180 / 4
[tex]\Large\boxed{x=45^\circ}[/tex]
Substitute the x value into the expression to find the third angle
Third angle = 2x
= 2 (45)
= [tex]\Large\boxed{90^\circ}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
find a number which decreased by 21 equals twice the opposite of the number
The required number is 7. The expression formed with the given information is x - 21 = 2(-x).
What is an expression?An expression is the combination of variables, constants, and coefficients.
If two expressions are related by an equal in between them, then that is said to be an equation.
Calculation:From the given data,
Consider the required number = x
The number is decreased by 21 i.e., x - 21
Twice the opposite of the number = 2(-x)
So, on equating,
x - 21 = 2(-x)
On simplifying,
⇒ x - 21 = -2x
⇒ x + 2x = 21
⇒ 3x = 21
∴ x = 7
Thus, the required number is 7.
Check:
7 - 21 = -14 and 2(-7) = -14.
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[tex]\lim_{x \to 0 (\frac{x(x-2)}{2-2e^2x} )[/tex]
Help evaluting this limit
Answer: 0
Step-by-step explanation:
Substituting in x=0, we get
[tex]\frac{0(0-2)}{2-2e^{2}(0)}=0[/tex]
giving brainliest!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: [tex]\pm1,\pm3,\pm5, \pm15[/tex]
Step-by-step explanation:
We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure [tex]\frac{p}{q}[/tex], where p is any of the factors of the constant term and q is any of the factors of the leading coefficient.
In this example, -15 is the constant term and 1 is the leading coefficient ([tex]x^4[/tex] has a coefficient of 1).
The factors of -15 are [tex]\pm1,\pm3,\pm5, \pm15[/tex], while the factors of 1 are [tex]\pm1[/tex]. p is can be any one of the factors of -15, while q can be any of the factors of 1.
[tex]\frac{\pm1,\pm3,\pm5, \pm15}{\pm1}[/tex]
The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are [tex]\pm1,\pm3,\pm5, \pm15[/tex].
Answer the journal prompts according to the scenario below:
Joe-Bob wants to buy a car and will need to take out a loan in order to make the purchase. His current monthly income is $3,500 per month. His mortgage payment is $900 per month, and his student loan payment is $350 per month.
Note: You do not need to take taxes into consideration for this journal.
According to the affordability formulas given, can he afford to take out another loan?
When should he follow the affordability formulas? In what cases should he not?
How could taking out the car loan impact his other priorities?
1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.
2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.
3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.
4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.
What is affordability?Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.
Affordability can be measured as a Debt To Income (DTI) ratio.
Data and Calculations:Current monthly income = $3,500
Monthly mortgage payment = $900
Monthly student loan payment = $350
Total monthly debt payment = $1,250
Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)
Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.
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Find the last number of the following series
10 8 16 13 39 35
1)75
2)100
3)130
4)140
The answer is 4) 140.
If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.
10 - 2 = 88 × 2 = 1616 - 3 = 1313 × 3 = 3939 - 4 = 35The next step, according to the pattern, would be to multiply 4.
35 × 4140J(1)²,
x ≤ 0
x > 0
2²,
Complete the table of values for function f, and then plot the ordered pairs on the graph.
-2
-1
0
1
2
f(x)
=
X
f(x)
Drawing Tools
Select
Point
Open Point
>
O
Click on a tool to begin drawing.
-10
-8
-6
-4
-2
10
8
6
4-
2-
-2
पं
CC
f(x)
Delete
2
4
Undo
6
3
+00
8
Answer:
1/4 ,- 4, 1/2 2 1/2 4 1/4
Step-by-step explanation:
1/4, 4 1/2, 2,1/2,4, 1/4,
If t1 = 4, s1 = 5, and s2 = 2, determine the value of t2.
Answer:
t2=8/5
Step-by-step explanation:
using this formula
t1/s1 =t2/s2
4/5=t2/2
cross multiply
5t2=8
t2=8/5
The correct answer for the value of t₂ is [tex]1.6[/tex].
Given:
Time t₁ = 4,
Distance s₂ =2
Distance s₁ = 5.
To find value of t₂ , use the concept of proportion:
[tex]\dfrac{t_1}{s_1} = \dfrac{t_2}{s_2}[/tex]
Put value of [tex]t_1 ,s_1 ,s_2[/tex]:
[tex]\dfrac{t_2}{2} =\dfrac{4}{5}\\\\t_2 =\dfrac{8}{5}\\\\ t_2 = 1.6[/tex]
The correct value of [tex]t_2[/tex] is [tex]1.6[/tex].
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Solve the system of equations algebraically and create a graphical model.
[tex]3x + 2y = 8 \\ x + 2y = 4[/tex]
Answer: [tex]x=2, y=1[/tex]
Step-by-step explanation:
Subtracting the second equation from the first yields [tex]2x=4 \longrightarrow x=2[/tex].
This means that [tex]y=1[/tex].
So, the solution is [tex]x=2, y=1[/tex]
I roll two dice and observe two numbers X and Y . If Z = X − Y , find the range and PMF of Z.
[tex]X[/tex] and [tex]Y[/tex] are independent and identically distributed with PMF
[tex]\mathrm{Pr}(X = x) = \begin{cases}1/6 & \text{if } x \in\{1,2,3,4,5,6\} \\ 0 & \text{otherwise}\end{cases}[/tex]
If [tex]Z=X-Y[/tex], then [tex]Z[/tex] has range/support
{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
where we can get
-5 = 1 - 6 in 1 way, hence with probability 1/36-4 = 1 - 5 = 2 - 6 in 2 ways, with probability 2/36 = 1/18-3 = 1 - 4 = 2 - 5 = 3 - 6 in 3 ways, with probability 3/36 = 1/12and so on, so that the PMF of [tex]Z[/tex] is
[tex]\mathrm{Pr}(Z=z) = \begin{cases}1/36 & \text{if } z\in\{-5,5\} \\ 2/36 & \text{if } z\in\{-4,4\} \\ 3/36 & \text{if }z\in\{-3,3\} \\ 4/36 & \text{if } z\in\{-2,2\} \\ 5/36 & \text{if } z\in\{-1,1\} \\ 6/36 & \text{if } z =0 \\ 0 & \text{otherwise}\end{cases}[/tex]
Sketch the region enclosed by the given curves and find its area.
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
How to determine the area of a region enclosed by four functions
In this question we must determine the area generated by four functions: three linear functions and a radical function. First, we plot the four functions to determine the required combinations of definite integrals need for calculation:
[tex]A = \int\limits^{0.382}_0 {[f(x) - g(x)]} \, dx + \int\limits^2_{0.382} {[h(x) - g(x)]} \, dx[/tex], where f(x) = √x, g(x) = x - 3 and h(x) = - x + 1.
[tex]A = \int\limits^{0.382}_{0} {[\sqrt{x} - x + 3]} \, dx + \int\limits^{2}_{0.382} {[- 2 \cdot x + 4]} \, dx[/tex]
[tex]A = \int\limits^{0.382}_{0} {\sqrt{x}} \, dx - \int\limits^{0.382}_{0} {x} \, dx + 3 \int\limits^{0.382}_{0}\, dx - 2 \int\limits^{2}_{0.382} {x} \, dx + 4 \int\limits^{2}_{0.382}\, dx[/tex]
[tex]A= 2 \cdot x^{\frac{3}{2} }|_{0}^{0.382} - \frac{x^{2}}{2}|_{0}^{0.382} + 3\cdot x |_{0.382}^{2} - x^{2} |_{0.382}^{2}+4\cdot x |_{0.382}^{2}[/tex]
[tex]A = 2 \cdot (0.382^{\frac{3}{2} }-0^{\frac{3}{2} })-\left(\frac{1}{2} \right)\cdot (0.382^{2}-0^{2}) + 3 \cdot (2 - 0.382) - (2^{2}-0.382^{2})+4\cdot (2^{2}-0.382^{2})[/tex]
A = 16.815
The area of the region enclosed by the curves x + y = 1, x - 3 = y, y = √x and x = 0 is 16.815 square units.
Remark
The statement reports an inconsistency with at least one function and needs to be modified in order to apply definite integrals in a consistent manner. New form is shown below:
Sketch the region enclosed by the given curves and find its area: (i) x + y = 1, (ii) x - 3 = y, (iii) y = √x, (iv) x = 0.
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a rectangular floor of a room measures 5.4m long and 4.2m wide .the room is to be covered with square tiles . Calculate the minimum number of the floor
Answer: 22
Step-by-step explanation:
Number of floor tiles = (5.4m × 4.2m) ÷ 1m²
Number of floor tiles = 22.68
Minimum number of floor tiles = 22
Help!
which of the following functions are graphed below
Which of the following represents all solutions to the equation
1/3x^2 +10 = 7
Answer:
1 +-3i
Step-by-step explanation:
Answer:
answer is 1) x=±3i
Step-by-step explanation:
